Kolmijako

#include <iostream>
#include <vector>

using namespace std;

int s(int n){
    return (n*(n+1))/6;
}

void pv(vector<int> v){
    for (auto & c : v){
        cout << c << " ";
    }
}

bool r(int n, int g1l, int g2l, int g3l, vector<int>& o){
    //cout << "n: " << n << " g1l: " << g1l << " g2l: " << g2l << " g3l: " << g3l << " vec: ";
    //pv(o);
    //cout << "\n";
    if (g1l == 0 && g2l == 0 && g3l == 0 && n == 0) {
        return true;
    }

    if(g1l >= n){
        g1l -= n;
        o[n - 1] = 1;
        n--;
        return r(n, g1l, g2l, g3l, o);
    }

    if(g2l >= n){
        g2l -= n;
        o[n - 1] = 2;
        n--;
        return r(n, g1l, g2l, g3l, o);
    }

    if(g3l >= n){
        g3l -= n;
        o[n - 1] = 3;
        n--;
        return r(n, g1l, g2l, g3l, o);
    }

    return false;
}

int main(){
    int n;
    cin >> n;
    vector<int> o(n);

    int bt = s(n);

    if(r(n, bt-1, bt, bt+1, o)){
        for (auto & c : o){
            cout << c << " ";
        }
    }else{
        cout << "IMPOSSIBLE\n";
    }
}

Test 1

Group: 1, 2

Verdict: ACCEPTED

Test 2

Group: 1, 2

Verdict: ACCEPTED

Test 3

Group: 1, 2

Verdict: ACCEPTED

Test 4

Group: 1, 2

Verdict: ACCEPTED

Test 5

Group: 1, 2

Verdict: ACCEPTED

Test 6

Group: 1, 2

Verdict: ACCEPTED

Test 7

Group: 1, 2

Verdict: ACCEPTED

Test 8

Group: 1, 2

Verdict: ACCEPTED

Test 9

Group: 2

Verdict: ACCEPTED

Test 10

Group: 2

Verdict: ACCEPTED

Test 11

Group: 2

Verdict: ACCEPTED

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: ACCEPTED

Test 14

Group: 2

Verdict: ACCEPTED

Test 15

Group: 2

Verdict: ACCEPTED